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There always seem to be a healthy debate over the correct multiple for the stock market.  The controversy is easy to fuel as the market’s PE ratio fluctuates over time and can be influenced by various factors.  In the end, the PE ratio is determined by what investors are willing to pay for earnings or perceived earnings.  Let’s look at a few factors which can determine the market’s PE ratio:

Using the average:

The simplest way to look for a fair or reasonable PE ratio is to examine history and find an average.  Based on trailing 4-quarter GAAP earnings and the time period between 1935 and Q1 2013, the average PE ratio for the S&P 500 has been 15.86 excluding the financial crisis in 2008 and 2009.  The Great Recession biases the data and tends to lift the PE ratio average.  The standard deviation of the average is 6.45.  Assuming the distribution of PE values is normal, about 68% of the PE readings will fall within one standard deviation or between 9.41 or 22.31. The graphic highlights the trend.

One could view the market as cheap or expensive as it moves outside one standard deviation, but this process will still create a lot of uncertainty over the fair PE value.  There is a lot of room between 9.41 and 22.31 and even a meaningful difference between 14 and 17.  With the S&P 500 expected to earn about \$100 per share on a GAAP basis in 2013, a one point change in the PE ratio equates to 100 S&P 500 points or almost a 6% move at 1700.

The current PE ratio for the 4-quarters through Q2 2013 is 17.62.  Based on current estimates and prices, it is expected at 16.74 at the end of 2013 and 15.15 at the end of 2014.

Looking at relative value:

It is awkward to compare a PE ratio to the yield on a treasury or corporate note.  It is difficult to relate a 20 PE ratio to a 5.00% yield.   However, to solve this problem many analysts look at the inverse of the PE ratio or the earnings yield (E/P ratio) and compare it to the yield on a fixed income product.    When a 20 PE ratio is inverted and becomes an E/P ratio, the yield is 5.0% and similar to a corporate or treasury note.   Investors treat the earnings like the coupon payment of a note or bond.

Given the Fed is buying treasuries and distorting the treasury market, it might be better to look at the relationship between the S&P 500 and corporate debt.  The Moody’s Baa corporate yield is a popular measure of corporate debt.  A Baa rating is neither highly protected nor poorly secured, and is a good representative of corporate debt yields.

It looks like the S&P 500 will post an earnings yield of 5.68% at the end of Q2 and this will compare to a Baa corporate yield of 5.19% at the end of June.  The current Baa yield is about 5.30%.  In recent history, since the mid 1950’s, it has been unusual for the S&P 500 earnings yield to be in excess of the Baa corporate yield.   However, before the mid 1950’s, the earnings yield on equity was persistently above   the yield on the Baa.

The graphic indicates that valuation can look cheap or expensive depending on the period of reference.  The average spread between the S&P 500 earnings yield and the Baa corporate is 0.16% between 1935 and Q1 2013. The median spread is -0.33%.  The standard deviation is a large 4.16%.  The current spread, about 0.40%, looks on the cheap side of the long term range, but not dramatically so.  Thus, even though debt yields are low and debt yields look uncompetitive, the earnings yield on the S&P 500 is not materially out of line with deep history and the market looks near fair value.

However, this conclusion changes dramatically when examining the data since 1970. The average spread between 1970 and Q1 2013 is -2.45% with a standard deviation of 2.40%.  At spread of 0.40%, stocks look at lot more attractive.   When “cherry picking” the data or analyzing the data in the memory period of most investors, stocks appear extremely inexpensive.

Doing some conversion and basing the PE ratio on the Baa corporate, one could argue for a PE ratio of 35 – very large.  The Baa corporate is about 5.30% and the average spread since 1970 has been -2.45%.  Adding these together, the earnings yield on the S&P 500 should be 2.85%.  In inverse of 2.85% is 35.  It is easy to see why investors think about 2000 for the S&P 500 and see the bull having legs.

Inflation:

Historically, there has been an inverse relationship between the PE ratio and the rate of consumer price inflation.  A low (high) inflation rate tends to see a high (low) PE ratio. The graphic seems to suggest the PE ratio should be higher given the low level of inflation.

Investors should be more willing to pay for earnings in a tame inflation environment. Low inflation can contribute to low interest rates, and benefit the value of financial assets.  The chart suggests that the PE ratio could easily expand a few points without suggesting overvaluation.

Looking at monetary policy:

Many in the market think the Fed is creating a bubble with its policy.  The chart following displays the relationship between the growth rate in reserve bank credit (assets on the Fed’s balance sheet) and the PE ratio on the S&P 500 based on operating earnings.  There is a loose, but positive looking relationship between the Fed’s balance sheet growth and the PE ratio.

The Fed has tended to be most easy with policy when the economy is weak and the PE ratio is rising due to a drop in earnings. The clearest example occurred during the Great Recession in the 2008 to 2009 period.   It seems like the relationship between reserve bank credit and the PE ratio was strongest between about 2000 and 2010.  In 2011, the PE ratio failed to expand materially with the surge in reserve bank credit.

The relationship suggests the PE ratio has room to rise, but the trade is probably ignoring some of the Fed’s activity thinking the expansion of the balance sheet is temporary and will eventually end.

The chart shows the PE ratio is not large compared for the last 20 years and the Fed may be having less of an impact on the market than many investors think.  If the PE ratio was 20 or 25, the Fed’s influence would be more apparent.  There is a great divergence between the expected PE ratio and current trend in reserve bank credit growth.

Concluding thoughts:

There are no easy answers when it comes to determining the correct PE ratio for the market.  The debate will rage on.

Looking at a long history of data, the S&P 500 seems like it is near fair value based on the average PE ratio and the earnings yield on the Baa corporate.  However, valuation becomes much more attractive if data only over the last 20 or 30 years is analyzed.

The Fed is not creating a stock market bubble given the relationship between the size of its balance sheet and the PE ratio. The trade seems to realize that the Fed’s action will not last forever.  This may imply that the impact of QE taper will be short term.  The market would probably be more vulnerable to selling if the PE ratio was closer to 20.

Low inflation tends to argue for an elevated PE ratio.  PE ratios can expand dramatically during periods of weak economic growth which have a disinflationary impact on the economy.

There is a good case for examining the PE ratio on a relative basis.  Valuation can be heavily influenced by inflation, Fed policy, and interest rates.

The market is not embracing the current outlook for earnings.  The expected PE ratio for the S&P 500 is declining into 2014. If earnings can just meet expectations, it may lift prices and the PE ratio.

An elevated PE ratio to average is justifiable in a low interest rate low inflation environment.   A GAAP PE ratio of 17 or 18 seems reasonable even if corporate yields rise another 50 or even 100 bps.

The S&P 500 is expected to earn \$111.53 in 2014 after earning \$100.94 in 2013 on a GAAP basis.  Earnings estimates are likely to slowly erode if history holds – analysts are usually too optimistic and this has been the trend over at least the last year. Arguably, think about 17 or 18 times EPS of \$105.00 or 1785 to 1890 for a 2014 fair value range.

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